Fuzzy Fractals and Fuzzy Turbulence

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 34, Issue 1, 2004, Pages 746-752

  Majumdar, Kausik Kumar ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Fuzzy differential inclusion (FDI) relations; Fuzzy dynamical systems (FDS); Fuzzy fractals; Fuzzy turbulence; Iterated fuzzy sets systems (IFZS)

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; FLUIDS; FRACTALS; FUZZY CONTROL; IMAGE ANALYSIS; ITERATIVE METHODS; PROBABILITY;

FUZZY DYNAMICAL SYSTEMS (FDS); FUZZY FRACTALS; FUZZY TURBULENCE;

TURBULENCE;

EID: 0742307281     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2003.811517     Document Type: Article

References (23)

1. M. F. Barnsley, Fractals Everywhere. New York: Academic, 1988.
2. R. A. Brown, Fluid Mechanics of the Atmosphere. New York: Academic, 1991.
3. C. A. Cabrelli, B. Forte, U. M. Molter, and E. R. Vrscay, "Iterated fuzzy sets systems: A new approach to the inverse problem for fractals and other sets," J. Math. Anal. Applicat., vol. 171, pp. 79-100, 1992.
4. R. L. Devaney, An Introduction to Chaotic Dynamical Systems. Reading, MA: Addison-Wesley, 1989.
5. D. Dutta Majumder and K. K. Majumdar, "Complexity analysis, uncertainty management and fuzzy dynamical systems: A cybernetic approach with some case studies," Kybernetes, submitted for publication.
6. G. A. Edgar, Measure, Topology, and Fractal Geometry. New York: Springer-Verlag, 1990.
7. L. V. Fausett, Applied Numerical Analysis Using MATLAB. Englewood Cliffs, NJ: Prentice-Hall, 1999.
8. J. E. Hutchinson, "Fractals and self similarity." Indiana Univ. Math. J., vol. 30, pp. 713-747, 1981.
9. T. Kapitaniak and S. R. Bishop, The Illustrated Dictionary of Nonlinear Dynamics and Chaos. New York: Wiley, 1999.
10. S. L. Loney, An Elementary Treaties on the Dynamics of a Particle and of Rigid Bodies. Madras, India: Macmillan India. 1972.
11. K. K. Majumdar, "One dimensional fuzzy differential inclusions," J. Intell. Fuzzy Syst., vol. 13, pp. 1-5, 2003.
12. B. B. Mandelbrot, The Fractal Geometry of Nature. New York: Freeman, 1982.
13. I. Milnor, "On the concept of attractor." Comm. Math. Phys., vol. 99, pp. 177-195, 1985.
14. H. T. Nguyen, "A note on the extension principle for fuzzy sets," J. Math. Anal. Applicat., vol. 64, pp. 369-380, 1978.
15. H.-O. Peitgen, H. Jurgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science. New York: Springer-Verlag, 1992.
16. S. B. Pope. Turbulent Flows. Cambridge, U.K.: Cambridge Univ. Press, 2000.
17. C. Robinson. Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. Boca Raton, FL: CRC. 1999.
18. S. K. Venkatesan, "Some vortex algorithms for 2D Euler flows," in Some Applied Problems in Fluid Mechanics, H. P. Majumdar, Ed. Calcutta, India: Indian Statist. Inst., 1993.
19. L. A. Zadeh, "Fuzzy sets as a basis for theory of possibility. " Fuzzy Sets Syst., vol 1, pp. 3-28, 1978.
20. [Online], Available: http://www.isical.ac.in/̃ecsu/kausik.htm
21. T. Sudkamp. "On probability-possibility transformations," Fuzzy Sets Syst., vol. 51, pp. 73-81, 1992.
22. A. Kandel. Fuzzy Techniques in Pattern Recognition. New York: Wiley, 1980.
23. K. K. Majumdar, "A mathematical model of the nascent cyclone," IEEE Trans. Geosci. Remote Sensing, to be published.